PLAISTOW, N.H. — Tips from acquaintances and others helped authorities track a fugitive New Hampshire couple to Florida, where they were arrested at the Universal Studios theme park on charges stemming from the beating and burning of the woman’s 3-year-old son, an official said Thursday.

Federal marshals took 23-year-old Jessica Linscott and her boyfriend, 27-year-old Roland Dow, into custody Wednesday evening at the Orlando park. They had been on the run for two weeks, making stops in New York and New Jersey on their way south, U.S. Deputy Marshal Jeffrey White said.

“They didn’t resist. They didn’t have any weapons,” he said. “I don’t think they believed anyone would come looking for them in Florida.”

They are due to appear in a Florida court this morning. If they waive extradition, New Hampshire law enforcement officials will escort them back to the state.

Police say Dow hit James Linscott hard enough in the head on Nov. 12 to cause traumatic brain injury and seizures and also burned his fingers and wrist. It was at least three days before the boy was taken to Exeter Hospital, where officials called police.

Police say Dow and Linscott told them by phone that the boy’s injuries were self-inflicted and that they would go to the police station later. They never showed.

Dow is charged with first- and second-degree assault. He and Linscott face multiple charges of child endangerment for failing to protect and get medical attention for James, who remains hospitalized at Children’s Hospital at Dartmouth in Lebanon.

A spokeswoman for the state Division of Children, Youth and Families, which has legal custody of the boy, would not comment on his condition Thursday, citing confidentiality laws. She also would not say whether the division had previous contact with the family. The boy’s father died of a drug overdose, Dow’s grandmother told The Associated Press.

Police say his condition is improving but that his recovery will be long and difficult.

“It’s very upsetting to everyone involved,” White said. “They were hiding out in a place you’d normally take your kids for enjoyment, to have a good time. Here they are down there, on the run, after harming their child.”

White said he is not sure what mode of transportation they were using and that both their cars were accounted for in New Hampshire.

“I think they were smart enough to dump their cellphones,” White said, stressing it was tips from acquaintances that led police to them.

“At one point in time they were still in contact with family members,” he said.

White said tips led investigators first to Florida, then to the Orlando hotel where the couple was staying, and ultimately to Universal Studios, where they were arrested after watching a parade.

Law enforcement officials spent “countless hours” trying to find Linscott and Dow, who are from Plaistow, N.H., a town of about 8,000 residents in Rockingham County on the Massachusetts state line, marshals said.

The Orange County Jail in Florida, where they are being held in protective custody, said the couple had declined all interview requests.

Dow’s grandmother, Helen Fram, who lives next to the couple in a two-family home in Plaistow, said Thursday that she’s certain her grandson and Linscott did not hurt James. She said the boy sometimes banged his own head on the bathtub or threw himself off the toilet.

“I can hear anything if anything is going on,” she said. “They would never, ever hurt a baby. Never.”

She said they initially went to the hospital with James but got scared when they found out police wanted to talk to them.

“They figured they didn’t do anything, so they took off,” she said.

Fram described her grandson as a loner and said he sometimes did siding or roofing work, though he is unemployed right now. She said she did not hear from him while he was on the run.

Asked why they would have gone to a theme park, she said that was one thing she did not understand.

In the small downtown of Plaistow, Joe’s Barber Shop owner Dan Diemand said every third or fourth customer for the past week has wanted to talk about the case, wondering if Dow and Linscott had been caught. A lot were angry.

“Especially parents, I think they take it very personally when a child is hurt,” he said.